The Poland international is widely regarded as one of Europe's premier strikers, and has been linked with a move to the Premier League for the last few months. The Daily Mirror carries the same report from Goal.com which suggest Lewandowski is set to leave Dortmund next summer.
But Michael Zorc, Borussia Dortmund sporting director, denied speculation that transfer negotiations have already taken place with potential suitors.
Zorc told Spox, and is quoted on Goal.com, saying: "As it stands there is neither a request nor a formal offer for Robert Lewandowski, [so] how could we have possibly rejected anything?"
But Goal.com carry a report from an alleged Dortmund official who says Lewandowski will leave the club at the end of the season.
"We do not know where he will go but the departure of Robert Lewandowski [at the] end of the season is a done deal," the anonymous board member reportedly said.
Manchester United can expect competition for the signing of the Polish star though, with Serie 'A' champions Juventus also reportedly interested in the Borussia Dortmund frontman.
Lewandowski has refused to extend his contract with the Bundesliga champions beyond 2014, and although the forward could move in January, it seems the German side are resolved to keep hold of him until the end of the season.
United already have fierce competition for places up front, with Wayne Rooney and Robin Van Persie leading the line most often, but Danny Welbeck and Javier Hernandez both push hard for starting berths.